Can kids have plaque in their carotid arteries if our family has familial hypercholesterolemia?

Yes. It is entirely possible to form plaque very early in life. Even persons without familial hypercholesterolemia form plaque in their aorta in their 20's as evidenced by autopsy series.
Possibly. It really depends on their level of cholesterol. Plaque has been previously reported in kids. I would recommend seeing a lipid specialist.

Related Questions

Is there a way to prevent my children from inheriting familial hypercholesterolemia?

Prevention. You can't prevent the inheritance of hypercholesterolemia because it is genaticicallty determined but your children can be treated with statins to control their cholesterol level. Read more...